# Random planar graphs

Marc Noy1

Universitat Politècnica de Catalunya

Let be a graph chosen uniformly at random among all labelled planar graphs with vertices. Which are the typical properties of such a random planar graph?

We show that has about edges, where is a constant completely determined, and that deviations from are with high probability of small order. Among other properties, we also show that is connected with probability tending to a constant

The basic technique we use in the proofs is singularity analysis of counting generating functions, considered as complex valued functions.

#### Footnotes

... Noy1
joint work with Omer Gimenez

2005-05-23